let X, Y be set ; [:X,Y:] --> (1. Z_2) is incidence-matrix of X,Y
set f = [:X,Y:] --> (1. Z_2);
( rng ([:X,Y:] --> (1. Z_2)) c= {(1. Z_2)} & {(1. Z_2)} c= {(0. Z_2),(1. Z_2)} )
by FUNCOP_1:13, ZFMISC_1:7;
then
( dom ([:X,Y:] --> (1. Z_2)) = [:X,Y:] & rng ([:X,Y:] --> (1. Z_2)) c= {(0. Z_2),(1. Z_2)} )
;
hence
[:X,Y:] --> (1. Z_2) is incidence-matrix of X,Y
by FUNCT_2:def 2; verum